(2m+3)(4m-1)=0

Solution for (2m+3)(4m-1)=0 equation:

Simplifying
(2m + 3)(4m + -1) = 0

Reorder the terms:
(3 + 2m)(4m + -1) = 0

Reorder the terms:
(3 + 2m)(-1 + 4m) = 0

Multiply (3 + 2m) * (-1 + 4m)
(3(-1 + 4m) + 2m * (-1 + 4m)) = 0
((-1 * 3 + 4m * 3) + 2m * (-1 + 4m)) = 0
((-3 + 12m) + 2m * (-1 + 4m)) = 0
(-3 + 12m + (-1 * 2m + 4m * 2m)) = 0
(-3 + 12m + (-2m + 8m2)) = 0

Combine like terms: 12m + -2m = 10m
(-3 + 10m + 8m2) = 0

Solving
-3 + 10m + 8m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3 + -2m)(1 + -4m) = 0

Subproblem 1
Set the factor '(-3 + -2m)' equal to zero and attempt to solve:

Simplifying
-3 + -2m = 0

Solving
-3 + -2m = 0

Move all terms containing m to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2m = 0 + 3
-2m = 0 + 3

Combine like terms: 0 + 3 = 3
-2m = 3

Divide each side by '-2'.
m = -1.5

Simplifying
m = -1.5
Subproblem 2
Set the factor '(1 + -4m)' equal to zero and attempt to solve:

Simplifying
1 + -4m = 0

Solving
1 + -4m = 0

Move all terms containing m to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4m = 0 + -1
-4m = 0 + -1

Combine like terms: 0 + -1 = -1
-4m = -1

Divide each side by '-4'.
m = 0.25

Simplifying
m = 0.25
Solution
m = {-1.5, 0.25}